Wanaka Search and Rescue responded around 10.45am. Three helicopters were used to assess the scene and get the injured climbers off the mountain.
They were taken to Dunedin Hospital with moderate injuries. Vink said they had broken bones and probably wouldn't have survived had the other party of climbers not come along.
"They were very fortunate we're not dealing with a double fatality ... that's great.
"Wanaka Search and Rescue have done a great job in terms of managing two patients in that environment."
Vink said the conditions were mild with light winds and sunshine.
Chief pilot Graham Gale said they came prepared to winch them up but found a small platform they could land safely on to reach the injured people. They had four medical professionals on the helicopter.
Gale said the rescue was "pretty straightforward".
"It's what we do. It was the best level of care they could get in a remote location."
Mt Aspiring is known to be a technically difficult climb. A 24-year-old woman died last year when she fell crossing a waterfall face in Mt Aspiring National Park. A 21-year-old man slipped and fell to his death in 2014. In 2005, three people died on the mountain in 10 days.